**
Below is the ascii version of the abstract for 98-710.
The html version should be ready soon.**Mohamed Sami ElBialy
Sub-stable and weak-stable manifolds associated with finitely
non-resonant spectral decompositions
(162K, AMS-LaTex2e)
ABSTRACT. In this work we study $C^{k,s}, 2\leq k \leq \infty , 0\leq s \leq 1$,
maps of a Banach space near a fixed point. We show the existance and
uniqueness of a class of $C^{k,s}$ local invariant submanifolds of the
stable manifold which correspond to a spectral subspace satisfying
a finite non-resonance condition of order $L \leq k$ and an overriding
condition of order $L\leq k$ (condition (3) of Theorem 1).
We study the dependence of these invariant manifolds on a parameter
that lies in a Banach space.
We also show that a $C^{k,s}, 2\leq k \leq \infty , 0\leq s \leq 1$,
local weak-stable manifold that satisfies these two conditions is
unique.